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3 years ago

Find the slope and y intercept

Mathematics

1 answer:

alexgriva [62]3 years ago

7 0

Slope: 5/1 (5 if simplified)
y-intercept: 10

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You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago

Solve for x and y. What is m

irina [24]

3x + 2y + y - 3x = 180

3y = 180

y = 180/3

y = 60

3x = y - 3x

Let y = 60

3x = 60 - 3x

3x + 3x = 60

6x = 60

x = 60/6

x = 10

Answer: x = 10, y = 60

4 0

3 years ago

Find the midpoint of the segment with the following endpoints (-10,-1) and (-6,7)

Gala2k [10]

Answer:

(-8 , 3)

Step-by-step explanation:

(x1 , y1) (x2 , y2) = (-10 , -1) (-6 , 7)

$\frac{-6-10}{2}$ , $\frac{7-1}{2}$ -6 is going to be my x1 and -10 my y1

7 is going to be my x2 and -1 my y2

(-8 , 3)

7 0

3 years ago

Which set of ordered pairs does not represent a function?

weqwewe [10]

Answer:

{(0,0),(0,1),(1,2),(1,3)}

Step-by-step explanation:

If this was a function it would be (0,0) ,(1,1), (2,2) ,(3,3) and so on

4 0

3 years ago

Question 1 of 14

Irina-Kira [14]

question seems incomplete

there are no notations for inequalities

8 0

2 years ago